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COE Combinatorial Modeling System is divided into non-overlapping modules Each module is assigned either a probability of working, P i, or a probability as function of time, R i (t)….(Reliability = 1- (area under the failure density curve) The goal is to derive the probability, P sys, or function R sys (t): Prob that the system survives until time t Assumptions:  module failures are independent  once a module has failed, it is always assumed to yield incorrect results  System considered failed if it does not contain a minimal set of functioning modules  once system enters a failed state, other failures cannot return system to functional state Models typically enumerate all the states of the system that meet or exceed the requirements for a correctly functioning system Combinatorial counting techniques are used to simplify this process

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COE Series Systems Assume system has n components, e.g. CPU, memory, disk, terminal All components should survive for the system to operate correctly Reliability of the system where R i (t) is the reliability of module i 123n R sys = R 1  R 2   R 3 ...  R n

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COE Non-Series-Parallel-Systems (cont.) For complex success diagrams, an upper-limit approximation on R sys can be used An upper bound on system reliability is: ABCD A F E C D D D D X Y Reliability block diagram (RBD) of a system R path i is the serial reliability of path i The above equation is an upper bound because the paths are not independent. That is, the failure of a single module affects more than one path.